{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "mu_space = np.linspace(-6, 6, 200)\n",
    "sigma_space = np.linspace(-6, 6, 200)\n",
    "mm, ss = np.meshgrid(mu_space, sigma_space)\n",
    "\n",
    "def neg_log_likelihood(x, mu, logsigma):\n",
    "    x = x.reshape(-1, 1, 1)\n",
    "    return np.mean(logsigma + (x - mu) ** 2 / (2 * np.exp(logsigma) ** 2),\n",
    "                   axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mu = 0.5\n",
    "sigma = 0.1\n",
    "\n",
    "rng = np.random.RandomState()\n",
    "x = rng.randn(1000) * sigma + mu\n",
    "nll_min = neg_log_likelihood(x, mm, ss).min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MeUXNgXf2rnY4uNnhaMgysu7T0xRN75SEEBTnlJAWp345UvakkxaXSXmRGgRm\nZqbgFeZB8KAAAmP8CBroh0+4Z6ea6VR1pJp1329h5SdryDiQTS8bay6+fSxT77uozXfa2pR8Hoyd\nja2LDe9vnd8ppwfv+iuOZye/wpApMcxd/lib7syamprYs2Y/v3ywil2r4jDvZs7QywcyZeZE+o8O\n61Q7zsryoyTvSid5Vxopu9NJ2plmnKBhZqbgFuhKYLQvgdF++A/wwa+/V6d8P9tKW54hXAO8AWwA\nFGAE8LgQYlkbtPOMNHcZNTU1cbik0hhyV5JXRmlec45RKTptKaV5ZVSWVx33GD179zAu2nDyUDOL\nHAyBd46GLKPOeFTckUryy0jbm0nSzlQ1/XRnmvFv2ZwXExobSPDgAEKGBHaKC+0IIUjYlsKvH/zJ\npmXbQQiGXTmYax6betwFhc7FvvWHeOqilxg4KZLnf3miU+0EtakF3D/oKZy9HHl3y4ttlt3fUN/A\n2sVbWPbW72QnaLF17suUey7ikrvGd4r3Xq/Xkx2vJXF7Ckk7UonflkJu0n+XVnEL0BA82J+gGH+C\nBvrh29+703ePtrW2LAj7gQnNZwWKojgC/5gi7fRMxxDqa+uNGUY6bamaY9T8L7eU4mzdCYPvetv1\nwsnTQY2g8Gy58s/JyxEbxz6dcuCovQghKMwqNkYKJ2xPIW1vhnFltouPE/2GBxM+PISwYUF4BLuZ\ndEep05by+4K/WPHJGqoOVxM1Lpwbn7mKiFGhbfK+/frhKhY8+CU3z72G6XOvPqvHEEJwaEsSW37e\nQWNDI3Yutlx8x9iz3sHWVNXyYOxsygoqWLDrVVy8nc7qcY5VW13Hn5//w9I3f6ckrwzfCC+ufmwq\no66JNWn3bG11Hck70zj0rxqymLA1herKGkCNkwmNDSRkiHrAEhjte0GkAhyrob6BEm2ZMYLHqpcV\nI68a0mYF4aAQIvyYn82A/cfe1lHaY1C5uWgU55Yc80fUUZxbQlGWjqJs3XER25ZWFjh7ORqXiasr\nCJ2Mt/V1OP8LRn1tPWn7skjYmkz81mQObU40Ftc+9r0JHxFM/9H96D86DO9+HiYpENWVNfzx2T8s\ne+t3ygor6Dc8mFuev5bIMec2U1oIwRu3LeCfbzfxyl/PED3hzI6NKsuPMvfy1zm4ORGL7hZYWXen\nsuwoFt0tuGH2ldw0Z9oZt6d5euzZtOf/1VbXseLjNfz0+q9U6I4QPjKE65++kpiJ/U3yua45WkPC\nthT2rY+NQUe0AAAgAElEQVRn/wY1I6v5YMQ7zIN+w4MJGxZMyJAAXP1czvvvXmNDIzptqXH/VJBR\nRGFmMYVZxRRl6SjNL2+x0DV4kD8f7ni1zQrCG0AE8IPhpmuBA0KIJ8/+JZ0dU8wyEkJQWXZULRS5\nJRQbsoyKcnTqm5BZbLxOQDMr6+5q4J2vMxofZ2OGkYuPE87eTudl6J0QgrzUAg79m8zBzQkc2JhA\nYaY61NTbrhf9R4cxYFw4UeMjcPPv2C9tfW09qxau48dXf6Ekr4zIMWHc8cqN59SVVFtdx/2DnuJw\nSSWf7nsDO5fWHdnX1zXw1MQXSdqRysy3b2XCLaPoYW1FfnohC2d/z6al23j4s5lccue4Vrdl9aL1\nvHn7R9w87xqmP3d2Zyyg7mhWLVzHdy8spaywggETIpg+Zxr9hnfsyub6ugaSdqSy9+8DxK07SPKu\ndPSNesy7mRM00I+IkaH0Gx5MSGzgeRlvLYSgsvwohZlqTlp+WiH56YUUZqp5RrrcEuMsKFDHRBw9\nHHD2NhykeqnJzM5eDmo3uLsdVj2t2nRQ+Sqg+VJKm4UQv5ztiz0XnXXaadXhKgoyiynOLjFWaTWN\nsIiC9CLjpfrAEHrnbofG1xlXPzXLyD1Qg1uABlc/Z7r3OH/6NouydRzYmGBIPz1IcU4JoIbbRY+P\nIObiKKInRHTYKX19bT0rP/2bH17+mQrdEUZdE8udr9501t0rWfG53D/oKSJGhTL/j9mtKnKLX1rO\noud+ZPb3DzHmupZXJ9Pr9Txz6Ssc3JTAF/HvtGpQPC+tgJlRjxM00J/X/p5zVumfQgi2r9zDZ49/\ngzalgH7Dg7l9/g0dFnEhhECbks+uVfvYvWYfBzclUltdh5mZQuBAfyLHqGeaYUMDz5trGgshOFxy\nhHxDQkFeagF5aYakgvQiqg5Xt9je1rmvGmnh43RMb4SaaeTk6XDaLjwZbtdJCCEoK6ygIN2QY5RZ\nTH6G+qbnpxUaL+3XzN7VVi0SARrcDTlGHsGuuHg7demkx+YziLh1h4hbe4C9/xyk6nA1ZmYKwYMD\n1PTTKdH4Rni1+9lDdWUNS9/8naVv/k5Tk+Cax6Zy3dNXnNVA428L/uLDBxby4Ed3MWXmxFNuK4Rg\nuu99uAe58upfz55wG522lFv87+ey+ydx95s3n/Lx9I16Hhoxh7yUfD7d/9ZZTffMTc5jwayv2LNm\nPx5Brtz1+nSGTI5u9/egrqaOfesOsW3FHnav3kdRtg4AjyBXoif0J3KsWgS6ev9/zdEacpPzyU3K\nJzc5T93xp6rRNNVHaozbmZmb4eLtiKu/Cxrf/3oUNL5qqN25hvydc0FQFKUSdZrpcb8ChBCizzm1\n8Cx0xYJwOlVHqo1HCAXpReQZcozyUvI5XPLfRXu6WZij8XP5L/AuxB2vUPVfV0yE1DfqSdyRyu7V\n+9j11z5SdqcD4Ohuz+BLBzD0soFEju3XroOXOm0pC59ezNrFm3H2cuSBBXcy+JIBZ/QYTU1NajzE\n5kQ+P/g2Gt+TH9VnxedyV/gjPPL5TCbdcfIuoScmvMBh3RE+3ffmKZ/7x9d+ZeHTi3l68SzGXj/8\nlNv+v7qaOr6f/zM/vfEblj0sueX5a5l670XtOqW4vPgw237bxbYVu4lbe5C6mnp69LJiwPhwoidG\nMvDiyDYZDO9oQghK8sqMWUY5SXnGiJljs8jMzBRcfJwMvQEuhq5kNc/IxduxXf/28gzhPHCkrBJt\ncj45SWpErja1AG1yPnmpLXOMHNzs1ByjYHe8wjzUqIp+nl3q6KqssJwdf6h5+HvW7Ke2qg7rvj0Z\nfOkAhl8xmIGTotptquD+jfF8cN8XZCdoGX3dMO5//3b6OrT+eEenLeXOsIcJHuzPq6vnnPTo+u9v\nNvL6rR+yMOHdU4b1ffnM9/z0xu+sOPrtSQuiNrWAu/s/ysCLI5m7/PEzOqI/uDmRt+78mLzUAsZP\nH8mM16dj62zT6vufieIcHRuXbmfrbzuJ/zcZIQQuPk4MuTSawZOjiRgV2mXG1IQQFGXryDqUq8ZZ\nJOSSm5RHblK+cZYTGPKMgt0McfYaPILd8Ax2RePnYrLXKgvCeaw5niInQUtWfC65yWr4XU6itsWM\nKEd3e7wMOUbe/dSl916h7p0+WKy+tp69/xxky8872LZiN0dKK7Gy7s6QKTGMujqWQZOi2vw1NNQ3\nsOS131j80jJ62Vjz0Kd3M+zyQa2+/+8freaD+7/giUX3M+HmUSfc5pt5P/Hdi8v4o2bxKc98Vi1c\ny9t3fcK3GQtOeMQshOCJ8c+TujeTL+LfwcHVrlVtrKup48vZP/Dze3/g4uPEw5/NZMC4tp8sWJJX\nyoYlW9m0bJsxudYv0puhUwcy/MrB+IR7dvqZQBW6w2QcUONfsg7lkGU4+j92x998IOYe6IpXqJpl\n5Bnq3imnpbe2IHSeJadSq5mbm6tjDAEahl420Hh7U1MTutxSsg7lGEO5suJz2b/hLxrqDIF35mZ4\nhripuSzHZBm11xHi2bC0smTI5GiGTI5G36jnwKYENi7ZypZfdrDhx3/pZWPN8CsHM/6mkYSPDGmT\nKa0WlhbcNGcawy4fyBu3LWDelW8w6Y5x3PPura1aqDh55gT++W4jnz3xLbFTY054dlZZfpSefXqc\nthusj706c+ZoeRV4H//7TUu3sW99PA8uuLPVxSDzYDbzr3+X7AQtl913MXe8emObLsCsOlzF5uU7\nWPv9Zvavj0cIgX+UD7fPv4FR18Ti6ufSZs/VlvR6PdrkfNL3ZZG+X83+ytif1SLSojnIbvz0kcY8\nI69Q9/NyZXOXOkNw6eMmZk19ElsXGzXL6P/yjHr0urBXGJ+MXq+nIL2I9P3ZZOzPIt2Q4tg86wfA\nTmOr5hf198YvSs0ycvJ06FRHOvpGPXHrDrF28Sb+/WUnNUdrcfZyZOIto5l46+g2639uqG/gm7k/\nseT13/AMcWPOT4/gFepx2vulxWVyb8yTTHtkMjPeOH5A+P17P2fz8u0sLVp4ysfZ8ccenp3yKh/u\neIWggf4tfldTVcsdIQ/Rx6E3C3a9etpZRUIIVn2xlgWzvqSXjTWPfXUfAy+KPO1raY2mpib2b4hn\n9aL1bF62nfraBlz9XRh7/XDG3TQS9wBNmzxPW2mobyDrUC6pezNJi8skfX8W6XGZ1NXUA2Bh2Q2P\nEDdjnpFvf298wj2xdepaQXYncl6eIQghSNieSnlhhfFNPJZ1355qZpGbPQ7udmqekaFoNGcZ9XXo\n3aniBjqCubk57oGuuAe6MurqWOPtleVHyTiQTXpcFqlxGaTuyWDnqjia9E2AemQUONCPwGg/Y5ZR\na+fbtwfzbubETOxPzMT+1H5cx9Zfd7J60Xq+e3EZ3724jOiJEVxy1wRip0Sf0wCdhaUFd7xyI1Hj\nwnnlpve5f/DTPLHofkZcNeSU9/OP8mHiLaP55f0/uWTGhON2iOYW5i3Gfk6meRtzi+N39sveWoFO\nW8rs72edthjU19bz/r1fsHrRegZMiOCpbx5okzPB8qIKVn+1nj8+/4fCzGJ62Vgz8ZbRXHTbGIIG\n+neKgwi9Xk9OYh7Ju9JJ25tB8q400vdlGf+2PXv3wLe/F5fcNZ6AAb74R3njEezWqXK6TKFLnSE0\njyEIIag+UkPJsVlGBeWUaEsp0ZZRkl+GLreUiuLDLRZwgHoUYO9mZ8gyslcXbrjZHZNnZE8f+96d\n4kNtCnU1dWQcyDF8idRwsJxErfHv6OTpoEYDDA4kaJA/AQN8TD4mUZxbwuov17Nq4Vp02lLsXW2Z\nfPdELp0x/px3gCX5Zbww7U0St6dy87xruGnOtFN+NsoKy7kl4AEGXzqAZ398pMXvFs35kR9e+ZlV\n9T8aD0r0ev1xO/bmweevUz9o0dVypLSS6b73MWBCBHOXPXbKdpcXH2bu5a+RuD2VG5+5iunzrj6r\nNQrNhBAk7kjltw9XsWnpNhob9PQfHcYld45j2BWDTL5+prz4sDHLKHF7Csm70qk5WguoEdYB0b4E\nxfgRNNAf/wE+aHydL6gDw/PyDKGZoihY9+2Jdd+eeIW4n3Q7faOe8qLDlOaXodOWGYLv1GKh05Zy\nYFMiJXllxiPiZt17WKoFw9PBGEfh5OGAk6eaZ+TgZnfeHkl079GdkMEBhAwOYMo96m01VbWk78tS\ns4x2pBC/NZkNS7YC6nTYgGhf+g0Lpt/wEEKHBnZ4VryThwPT517NDc9cyc5Vcfy24C++nruE7+cv\nZ8wNw5n2yBR8+nme1WM7uNrx5vrneffuT/lm3k8UZ+uY9cmMk77/di62XPXQZBbPX84Ns7PxjfAy\n/q6PQ2+amgRHy6voY9+bgswiZkY9To9eVgy8KJIHP74LC0sLDpeoESC97VpeWvL7l3+mtqqWW1+4\n9pRt1qbk8/Sk+ZQXVvDcssfO6aI++kY9m5dvZ9nbK0jelU7P3j2YPHMiU++9yGTXvG5qaiInMY+E\nbSkc2pLIoS1JFGQUAeoYmV9/LybcPIrgwQEEDfTHPVBzQe38a47WUpStozinBF1uKT3OYFr6+blX\nMzDvZo6Dmxp/HTTwxNvo9U2UF1Wgy1XPLnTaEopzSinOKaEoR0f6vqzjAvDMzBQc3O0Ny8Qd1QUk\nPk7q0nEvRxzc7Lr0IrL/18PaSt3hDws23lZaUE7SjlQStqUQvzWJXz9YxdK3VgDgHqghYmQo/UeH\nET4ytMPy8c27mRM7JYbYKTHkJufx6werWLNoA2sWbWDgxZHcMPvKs4phsOxuweNf3YezlyPfvbiM\n8uLDPLvkkZNOg73qkcn8+uEqvp67hOd/ecJ4u71hALgkr4w+9r1Z8tpvVB+pwS1Aw19frWfIlBiG\nXT6I8sIKLLpbtBiYLskv4/ePVjP+5lGnHM9I3ZvB7EnzAXhz/byzjueor61n9Vfr+emN3yjM0uEe\nqOGBD+9k/PSRHb7uRd+oJ31/Fgc2JnBgUwKHNica03dtHPsQNjyYKTMnEjIkAP8Bvud9kmlNVa0h\nFUFHUbYab1GQUaRG6mSXHBelEzKk9Z8Bk3QZGfKRpgD1QDpwmxCi4tT3Mt2005qqWvWsIrfUWHmL\nsnXqG5KloySvrEWYlHk3cxw97NH4OqHxcUbj54ybn4v6s68z1n3Pv2sy1NfWk7Ing4StyRzcnMjB\nzYnG5fcuPk5EjunHgPERRI4J69AZTUfKKln5yd/88t4fVOiO0H90GDfPu4aIkaGnv/MJrPhkDR/c\n9wXhI0N4acVTJ41S+O7FZXw9dwmfxL2BX39vABK2pzBr6DO8+PtTDBgfzlWOtzPq6qE89OkMrnWd\nweBLB/DEovt5+cZ3SdqRxjdpHxof79PHvuHn9/5gUfL7J138lrAtmacnzaeXjTWvrZmDe6DrGb++\nupo6/vj0H5a88RtlBeUEDw7g+qeuYMiU6A47ym5qaiLrUC57/1GzjA5tTjJO93QLUA82woYFETY0\nCLcAzXnXvdvU1ERZQQUFGUXkGaIsjAF2mcXHHaBaWln8F2dxTI+GmmVkj73Glm4W3TrvOgRFUSYC\n64QQjYqivAbQmrC8zroOob6ugWJDgSjOLqEwW2dMHyxILzruDext1wuNr5Mxy8jN3wW3ABfcAzT0\ntut1XnzA9Xo9GfuzObgpkQOb4tm/IcF4dTbvMA8GjI8g5qL+RIwK7ZD+5+Yo5yWv/UpZYQVR48K5\n7aXrCRl85kfQ637YwmvT3ydiVCgvrXz6hO0/WlHFjV73EHtZDE998yCgji9c6zqD+967Hc9Qd56c\n8AIvrXiKwZdGM++qN8g8mMPXKR8wa/izWFh248118/57LO97GHTJAJ75/qETtilxRypPTXwRG+e+\nvLF2Lk4eDmf0mhobGvnz87Usnr+csoJyIseEccMzVxE5pl+HfB5L8krZ9dc+tQisPWhcpe8eqCFy\nTD/CR4YSMTIEB7fOdzW2s6HXN6HLLSEvtRCtIc4iP62I/IxCCjN1xmnioHaDOXk64GpIVXbxccTZ\n0xBk5+OErXPf0xbrLrMwTVGUK4BpQogbT7dtZy0Ip1N1pJqC9CLy04sMoXfFxqpflFXcYuDbum9P\nY3FQQ+9c8Qx2xS1Q06Uv3KPX60ndk8G+9fHErT3Awc1JNNQ1YNHdgvCRIQy6OIohU6Jx82/fqYp1\nNXWs/ORvfnz1Fyp0RxgxbQh3vHzDGT/v2sWbee3mDxh0SRTzfn78hGMKC2Z9ycpP1vBtxgIc3OwR\nQjC1z3Qm3TEORw8HPnv8GwZMiCAoxo/62gZ+ee8PVlYv5iYfdWroY1/eC8APr/zCl898z8d7Xsc/\nyue458mKz+WRkXPoZduLtzc+f0Y7TSEEW37ewRdPLyY/rZDwESHc8sK19B8VdkZ/jzPV2NBI/L/J\nbF+pZhllxecC6vTn6AkRRI7pR+TYfmdc2DoTIQQVxYfJScwjNzkfbUoB2pQC8tMLKcgoMkZ4g5qQ\n7OqnBl425xe5+Dji5u+Ck6fDOY9ZdqWCsAJYIoT47iS/nwHMAPD09IzOzs7uyOa1u4b6RgoyitCm\nFKiniKkF5KUVkZ9WQFF2SYuuKEd3e9wCNXgEqUXCM9gNz1B37DW2Xe6sora6jgMbE9j79352rd5H\nTqJ6hSv3QA2DL40mdmoM/YYHn9PMmFOpOVrDsrdWsvSt32msb+SKBy/hxjnTzqh/fOWnf/PePZ8x\n4ZZRPP7lfce9BwWZRdwa+CDTHp7MXa9PB+DuyMdw9LDHzV/Dys/+pt4wfdrKuju1VXUsSv2AWwMe\n4Jbnr+WmOdNobGjkJp978Qrz4LXVc45rg05byoOxs2lqEry75cUzumxo+v4sFsz6koObEvHu58Gd\nr9zIoEsGtNtnqbL8KDv+2Mu2FbvZs2Y/VYersbDsRvjIEKIn9CfmosgusYr5/zU2NJKXVkhOQh7Z\niVq0yfnkpqgF4NgAu+49LHELcMHNX2OMxHfzd8EtUNPu32GTzzJSFOUf4ETLE58RQvxm2OYZoBFY\nfLLHEUJ8BnwG6hlCOzTVpCwsu6k79hNk29TX1qsftEQ1LCsvtZDclHzWfb+lRTxuLxtrPIJd8Qhy\nNQTeeeDTzwNHD/tO++Wy6tmdQZOiGDQpiplAYVYx21fsYeeqvfy+4C+Wv7OSvg69GTI5hqGXDyTm\nosg2zYHp0asH0+dezSUzxvPlM9+z9K0VrP1+M/e8fSsjr45t1d9t8t0TKC+q4Jt5P+Ee4MoNs69s\n8XuNjzPDrhjEqoVrueWFa7G0ssTV34Xs+FxsnW0wM//vNL85ciQtLhMA737qwPH2lXsozS9n1scz\njnv+mqpanp3yCtVHanhnc+uLQXVlDYvm/MhvH66il20vHvzoLi65c1y7TIQoyS9jy/IdbP19Fwc2\nJqBv1GOnsWXktFgGTooiZmJEl4m0rq9rQJucT9ahXLITtWQnaMlNzic/rbDF0b6zlyNuARomTB+J\nW4AGz2A3PIJccXC36/SzndqtIAghxp/q94qi3ApMBsYJU5+mdFKWVpb49PM8bsqkEILyosNkJ2jJ\nTlQzVnKT89m9ej9rvt5o3M66b081yyjUQ80yCvfEJ8KLPv83nbEzcPF24vIHJnH5A5OoOVrDrr/2\n8e+vO9nyyw5WL1pPzz49iJ0ao+5ILo5ssxRUe40tj395H5PvnsgH933OS9e9w5DFm5j10V2t6nq5\nac40tCn5fPXsD/iEexI7peVB2OS7J7J52Xa2/LKTsdcPx9XPhR0r9xASG9iin7hZtqHrJGCAL6Dm\nGtm72jJoUlSL7YQQvHn7R2QdzOGllU+3mN56KjtXxfHuzE8p0ZZx6Yzx3Db/+ja/yExpQTkbf9rK\nlp93cGhLEkIIPILdmPbIZIZfOZjAGL9OvWNsamqiMLOY9P3ZaohdvFYNsksuQN+o7vjNzM1w83fB\nM9iNoVNj8Ar1wDNEjarvyl27phpUvhh4GxglhNC19n5ddQyhIx0pO0pOgpbMgzlkHMwhOyGXrHht\ni6lojh72+IZ74RPhiV+EF36R3rgFuHTKL2ljQyNx6w6xcclWtv62k8ryKnrbWjPiqiGMvXEE4SPa\nJssI1OmNv7z/J18/t4Rult247/3bGXfjiNOeLdTV1PHwyOfITyvk4z2vt5gF1NTUxM1+9+MWqOG1\n1XP457tNvHbzB4y5bhgblmzl/79/Y64fzu6/4lhe8hWFmcXcEvAANz57Fbc833LtwbK3V/DpY99w\n56s3ce0Tl532tVUdqeaThxfx11fr8Qp15+HPZhI2NOgM/jqnefzDVWz+eSfrf9zCvrUHaWoSePfz\nYORVsYy8JvaU64VMqaaqlswDOWqsywE1yyjzQI5xVpOiqJHVXqHuxoMq734euAVoukxKK3TyMQRF\nUdKA7kCp4abtQoiZp7ufo7VG3DX2Iew1ttg698Xe1RY7Y66RDXYaWywsz+ulFWel+SI9GQfUD336\nPvWDn5uUbzzisbLuTsAAH/wiffCP9MY/yhuvUPdOtQCvsaGRvf8cZN33m/n3153UVtXh7OXIhJtH\nMfGW0ae8FsGZyEsr4I3bFhD/bzKjrxvGQx/fddogs4LMIu6NfhK3ABfe3fJSi7/bty8s5Zt5P/FN\n2ofoG/XcFjyL2CkxbFuhHtzYu9lRmlcGqGcG1jY9eeOfuSx67kd+ePlnvsv6uMVajpQ96cwa+gyD\nJ0czd9ljpy1YCdtTeOXG9yjO1nHN45cxfd41bbIza2pqIm7tQf7+ZiObl6tZRhpfZ8ZeP5wxNwzv\ndEWg6nA1qXszSNuXRVpcFql7M8hNyjcWZeu+PfEJ98Q3wgu//uo/z1D3Ln3E36xTF4Sz5WrrIa4M\nuYXyogrKi44Yd2bHsnHqY1yM5uhubywW9q52hpwjuy55QZn2UF/XQE5iHmlxathX6t5MMg5kG/uz\nLa0s8B/gQ1CMHwEDfAka6NdpVn3WVNWy7bddrP56A3H/HEQIQdS4cC69azyxlw085x2eXq9nyWu/\n8fXcJTh5OjB32WMnnOFzrM3Lt/PC1W8x/bmruXneNcbbi3NLuMn7Xm6aM42bnpvGFXa34h/lw4GN\nCQA4eTtSnKVDMVOw7G7B5LsncPdbt3Br4AO4+Djx2prnjI9VW13HvdFPUHO0lk/3v3nK7h4hBMve\nXsnCpxfj6G7Hk98+2GJx4dkqyStl9VcbWLVwLUXZOnrZWDPmumFMuGU0wYM6R5ZRTVUt6XFZpOxJ\nJ2V3Bsm709GmFBh/b+9qi3+kD4ExvvhHeuMX6d3pwhzb0nlZEI7tMmpqauKwrpKywnJKCyoozS+n\nNL+MkvxySvLK0GlLKckr42hF9XGP07NPDxwN2UVOHuriDcfmIuJhj6O7Pd17dO5rBrQXvb6JvNQC\n0vZmkrJH/SKl7skwhgla9+1J8CB/QmMDCRroT8hgf2Ncs6notKWs/mo9f325jqJsHTZOfbn0rvFM\nnjnhnOetJ2xL5qVr3+FwyREe+fwext044pTbv3rz+2z4cSvvb5tPYLSf8fbHxs6jrLCCLxPe5bGx\n8ygtKEebnA+ArcaG8oIK40yjRxfeS8AAH2ZGPc7Dn83kkjv/u7rap499w7K3V/Da38+d8loGNVW1\nvHXHR2z8aRvDrhjEYwvvPacLJgkhOLApgd8W/MW/v+ykSd9E1LhwJt0xjmGXDzRpnlVTUxN5qYVq\njtHONBK2pZB5MMcYSWOnsSVkkD+BA/0IGOBDwABfbBw7/IKPJnXeF4TWqqupp9RQJEryyyjNL0en\nVTONinPVrI9jL1XZrK9Dbxw97HFuzjPycjAWDycPB/rYnx8LyFpD36gnJ0lNjkzamUbi9hSyDuUa\n10+4B2oMWUbBhA0NNNnqUb1ez95/DvL7R3+xY+VeFDOFEVcN5upHpx4XI30myosPM/+6d9i/IZ7r\nn76CW1+87qRnSZXlR7mz3yPYu9rywfaXjdNmf/1wFQse/JIvE9/lj0//5veP1xgHlS26W9BQ14CN\nUx8qio/w4Y5X2PLzDn5683d+zPvMGL+cFpfJfQOfZNKd43nok+NnHTUryS/juamvkhaXxR2v3Mg1\nj0896/ejvq6B9T9sYfk7K8k8mENvW2suvn0sk2dONNk1Dupr60nZncGhrcnEb0kifluKcYysZ+8e\nBA/yJ3iwP8GDAgiM8cVeY7qE3o7W2NBISV45utwS4z6ut20vJs8YLwtCa9XV1FOSX2bIMvqvWBTn\nlBhiKkqOi9vu3rM7zl4OuBiKRXOeUXMgXm9b6/O6YFRX1pC6J4PEHanEb00h/t+kFvky4SNCiBgV\nQsTIULz7eXR4N1NBZhG/L1jNqoVrqTpcTfiIEK5/+gpiLoo8q/elob6BD+9fyJ9frGX0dcN4/Kv7\nTtotte6HLbxy43s8uOBOptxzEaBeSvJG73u57aXrcXCz443bFhx3P42fMwXpRfxasYi7wh/FJ9yT\n+StnA2qxmzX0GYqyS/gy8V162554plh2Qi5PT5rP0fIqnvnhIQZfGn3GrxXU9/ePT/9m2TsrKSso\nxyfckysevIQx1w/v8KygmqpaEramsN+QZZSyK90YY+0R5ErY0CA1gXdIAB7Bbpibm75Ls73o9U2U\n5pcbo3PURAQdhVnFFGWXUJpfdlzCc9TYfry2arYsCG1FCMFh3ZH/CkWuGn6nhkupb8yx6wJA7ZZy\n8XbExdvJEFPhjKuvCxofJxw9zr+0VGMC5dYUDv2bxMHNiRRmqRPIetv1ImJECFHjw4ka2w+PINcO\nK5bVlTX8tXAdy95WryMQEO3LTXOmETsl5ozbIITgpzd+54unvmPA+HDm/fLECQcchRA8MeEF0vZm\n8nXaB8Z+/odHzuFoeRVPfH0/98Y8SfeeltRV/3eg4R7kSl11Hc8tfZQHhsxucTnO5kjsJ76+nwnT\nT3yJzqSdqcyeNB+L7hbM/2P2acc8TqTqcBU/v/cnv7z3B5XlVUSNC+eaxy8jekJEh71n9bX1JGxL\nYcje8b8AACAASURBVO/aQ+xbf4iU3RnoG/WYmZsRGONLxIgQwoYGERIbeF5cvOb/VVfWUJD5X2hd\nfnoRBYYco+Lc0hZjp4qiYO9qi4shWLO5R8PR3Q5HTwec3O2wsraSXUYdrbK8isLMYoqOCb4rzFLf\nxIITZZN42KPxdf5vtWKAC27+Lrh4O503M6UKs4oNWUaJ7Ft/yFgg7DS2DBjXz7A6tX+H9Oc21Dfw\nz7eb+OGVXyjIKCIwxo9bX7j2rM4YVi9az9t3fkz4yFBeXPHUCYtC5sFsZkY9zrRHphhXKf/y/p98\n9NBXfLrvTe6OfKzF7CIAOxcb/A193D+8/DNLixbSx7439bX13BY8i76OffhwxysnPNuK35rM0xe/\nhI1TX177e84ZrVgG9Sj853f/YNlbKzhaUUXs1Biuf/rKs8p6OlNCCLIO5bLzrzj2/n2QQ/8mUV/b\ngJm5GcGD/ek/Kozw4cGEDQs6byaEHK2oIj+9yJBjpAbY5WcUUpBRfFwXdh/7Xrj4OOHq46z2Rng7\n4eSlhtc5ezm2agKFLAidSFOTepqnZhmpp3n5GUXqv/Qi9dq5BmZmihpk5eeMW4AG9wAXPAJdu8xK\nx1PJTy9k37p44tYdZO/aQxwpVT/4AQN8iLkokiGXDiBokH+7nvLrG/X8/e0mFr+4lMIsHf1HhzHj\njektBoBbozngrv+Yfry04qkTDqq+evP7/PvzThalfoC9xpaCzCJu9rufe96+lZ/f+wMLKwu0yflY\nWllQX6seMMx4fTqblm9HUeD9rS8D/605ONlAcvLudJ4Y9zy2Lja8uW7uGQ2k6/V6/lq4jq/nLqG8\n6DBDpkRz89xrjAvj2kvV4Wp2r9nPjj/j2PP3AcoK1GsYe/fzYMC4cCLH9CNiVAjWfbpuMnBz0kBu\ncgHalHy0qYXkpRWQn17EkdL/1gUpitLiANHFEFrnavi5LdKRZUHoQo6UVho+LIYjhfRC49FDiyyU\nnt1x81cLhUegIc8o5H/snXd4FFUXxn+bRktI772HhNB7700QUKQoVXpHPnrvIEWaSBcQFARBFEU6\nBEINhISE9N57Dylb5vtjwmoMYoAAAfM+zz7J7t6dmZ2due85557zHnMsnUzfeteyF4VCoSDUO5L7\n5324f+ERAbdDUMgVaBto0bRHA1r2aULTHg1eW59sabGU33df4vtVP5GdlkuX4e0Ys/azF2oRevE7\nDzaM2kHz3o1YdnJ2GemH+LBERrt+wQfjujD16zEAjHSehoWTKRrV1fG54k9uZj42da2I8o8BYMOV\npcztupLBc/sxatUQCp8UMcx2EnYNbJ6pZRQTFM8XbRdTU6s6X11f+UK9J3yvPWbH9G+J9IvBrbUz\nY9YNrZC01H9CYkQyN3/x4u7v3vjdCEIuk6Olp0njLu406lKPpj0aYGCu99r2/7qQlZpDTGA8McHx\nxAYlEFsiYpcSU1qLzMBcDwtH0xIRO/Fh4WSKqa3Ra79/qwjhPcBTiYrY4ARiSjRT4kLFiy0p8k+V\nVBUVsZrS0lkkCOs6Fti4WWDlYv7OpM/mZubhdc6Xe2e98TrvS056LhrV1WnU2Z1WfZvSul/T15Le\nmp+dzw+rT/HztrOoV1dn1Moh9JnUrdyier9+c57tU/bRZ0I3pu4YUyb89NXYXVw6cp3vo75B11iH\nLeN3c+34LcatH8bm8buV42zdrUiOSmXStlFsHPUN226voU5zR87sPM+2yfv4ymMF7m1LN/fJTMlm\navP5FBUUs/XmqnJn/WQkZbLrf4e4evQmJjaGjF0/jLYft6jwNQJBEIj0i+H6ybvc/tWLiEci6dnU\ntaRZz4a0+KARri2d3plmUpnJ2aKURWAc0YHxooppSCLZf5G3r16rGhZOplg4mGLuaKIUojR3MKH6\nWyxwqyKE9xzFRVLiQxOJDownOiCe2JAEYgLjiQ9NVAptqahIMHMwwbqOuVLwztbdEjN7k0qdiSGX\nyfG/GYznz/e4c+Y+SVGpqKqp0rBTXdp+3Jy2Hzf/xyybl0VcSAJfT/uWBxd8cWnmwMx9E8vddnPv\n3CMc3/ALk7d+Tr+pPUu9Fxscz+d1ZijVS6//dJuVA79i0Y9fsGrQZgbO7otTE3uOrj2FtoEWmrqa\n+HsGcTR2F4Ig8LnLdLT0NNl+Z22pCbu4SMqcLssJ845kk8cKnJv8e8hLEATOfXuFPbMPU/SkiEFz\n+zF4Xr8K70cR6R/D1WOillFscAIqKhLcWjuLxN63aYVVlL8uFOQVEukfS5R/LFEl0i/RgXFkpfw5\n8Wvq1sK6RLTOqo451q4WWDmbVVpBySpC+I9CLpMTH55M9ONY8aJ+HEt0QDwJ4UlKj6JazWrY1rUQ\nhfPcRT0ju3pWlXLBThAEwh5G4nHiDtd/ukNiRDLqGmo069mQjkNa06J34wrzggRB4OpRT3Z+cZC8\nrHyGLxvEwNkf/qsFq1AoWPbRBu7+7s3GK8vKWPILeq0m7GEkRyK/QS5X8LHB5/SZ0A2vcw8xtTdm\n6U+z+LD2cD6e2Yezey7Spn8z/rd/krLyecmJ/9H24xaltrllwh5+33ORhUdn0GFQ63/9bmnx6Wwa\ns5P7532p196VGbvGVWhP5JSYNK4c9eTK0ZtE+sWgoqpCvfautPu4BW36N32jXfLKC0EQSI3LINw3\niohHMUT6xxDxKIaE8GRlqKeGZnWl123rbomtmyXWrhboGmtXyon/n/BeEoJ+TVNhSLsvMDDVQc+o\ntvgw1kbPuDb6xtroG2ujbaBVqa3ft4WigmJiguKVonfhPtFEPo5VFvRIJBLMHU1wbGhbouNig2Mj\nW7R0X766taIhCAKh3pFc+cGTqz/eIiMxk1raNekwqBXdR1acbEJWajbbp+zn+onb1G3jwrzD0zC2\nNnzuZ/Kz85ncbD6F+YXsergBHcM/0yG9L/sxt+sKZh+YTLcRHZjfcxXJ0Wm4t3HB48Rt1p1fxNQW\nCxizbij75h1h/pFpdPq0LbM7LyMpMoWDodtLhbA8jt9i1eDNDJrTlzHrhv7r97lx6i6bx+5EWiRj\nzJdD6TOxW4UkJxQ+KeLmz/e4cMiDh1f8EQQB15ZOdBzSmvaftKxUKaGCIJAQkUzYwyjCfaNL9Iwi\nS2X0mNoZY+duqdQysq1rhZGV/judyPEU7yUhWJnYCSO6ziE9KYuMlByy0/PKjFFRVUHfWBsDU20M\nTHUwNNNFr4QsDEx10DfRRt9E+51SKnxdEASBtPgMIvxiRLGvh5GEPYwiNS5dOcbUzhjnJnYleka2\nODa0eaux0KeQyxX4XnvMhUMeeJ66S1FBMdauFvQa25muw9pVSEjp0pHrbJ+8DxVVFeYcmlJG2vrv\nCPOJZFqLBTTtKXZRe0pOgiAw2nUGtQ202HJjFSc2/sqeOYeZ+NVIds48iI5hbbJScxi6eABHVv7E\n99E7ERQCQ20nMXLFYD5b9LFyH4mRyUxoOBtrVwu+8ljx3HqW4iIpe2Z9xy87zuHUxJ75R6a9VJ/l\nvyPiUTS/773MpSPXeZJTgImNId1GtKfLsPaY2hq98vYrAmnxGYQ8iFDKr4R4Ryqz+VTVVLF2Ncex\noS0ODW2wr2+DnbvVa0tgqAx4Lwnh7yEjmVROVlou6UnZZKRkk56UTVpSNulJWaQmZIm6RolZFBWW\n1Z3XMdDC0EwHA1NdjCx0MTTTLSEQHZE4jLXfmcWuikZOei6hD0ULKvhBBMFeYaTFi2mBKioSbOpa\n4trCCZdmDjg3tcfS6e02Os/PeYLHj7c5u/8ywV7hVKuhQadP29B3cndlg/uXRUJ4EisHfkXYw0iG\nLh7AsKWfPNdifJoi+r/9k+gxqqPy9WPrfmb/gh84HLGDrJRsprZYwKSto/hm+gEAxqwbSqRfND5X\n/TkWt4fDy0/w3fLjHI7YgYmNOMkKgsCcLssJuR/Bbt+NytefhbSEDFYM2EjgnVA+nvEBo9d99ko9\nJKTFMjxP3eWXb87z+GYw6tXUafdxc3qO7oR7u4qTIH8ZFBUUE+odSZBXGIF3Qwm695frVVUFGzcL\nXJo6lOgY2WLtavGfMwj/E4RQHgiCwJPcQtKSskhPEkkjNSGT1IQsUuMzSE3MIiUug8InpaUpVFQk\n6JvoYGShi5G5HsaWehhb6GFoLj43NNel+juSwVMRyEjKIsQ7gmCvCILuiTfdk9xCQKxEdm3hSN3W\nzri1dMKxke1bS4MN84nizM4LXP7+BkUFxbi3dWHAF71p3rvxS4cSiwuL2TppLxcOXqPtgBbMPTTl\nHxdiFQoFszotI8ovhv2BW5Vhk6c1CMOXDWTwvH70rT2cflN7MnLVEHLSctA11mGQ2VgadqnHvMNT\nGWY7GWs3C9b+sUi57bP7LrN53C5m7BrHB+O6/uPxhnpHsPjDdeRnP2HOwSll1h9eBDkZefy+5yKn\nvz5PRmImZvbG9JnYjW4jOry1RkuZydkE3AkRtYxuhRD2MEpZvWtsbYhrC0dcmtnj3MQeu3rW70ym\n3atCEASyM/JIicskNT6T1IRMkuMy0DXUYtCUblWEUF4IgkBedoHSs0gt8SxS4jJIiRdPalpillI9\n8Sm09TUxtighC0t9TK0NlP8bmeu+11aIXK4gNjiB4HthBNwJxf9WsFJeWF1DDacm9tRr60L99q7U\naeH4xvVvcjLyOH/gKr/sOE9ydCoWTqYMmtOXzp+1falK8KdS0nvnHMaluQMrf52HtsGzK6yjA+OY\n0GAWHQa3Zu6hqcrX53ZbQUJYEofCvmZ660Uo5Ap23FsH/LnOsOSnWWjq1GROlxUsOvYF7Qe2AsQU\n089dpmPfwIb1l5b8o0X+4KIvyz/eiJaeJit/nVfuTmp/R1p8Bj999Ru/771EYX4RjbvWo/+0XjTt\nUf+NewOpcen4eQbh6xGA340g4sOSAFEU0LmJHW4tnUT13Sb26BpXnnWLisbTeSo5Lp3kmAwSY9JI\njk0nKSaD5Lh0UuIyy2iuVa+pQZOOrizaM7qKECoScpmctESRMFLiS4giNoOU+AySotNJic8o1VdV\nIpGgZ1wbEyuRKEys9DGzMcTMxhATa31qv4fid1kp2QTcCeXx7RD8PIMI9Y5EIVegqqaKcxM7GnRw\no1Hnujg3c3hjZCmXyblx8i7H1v9CuE8URlYGDJ7Tl+6fd3ypY7hx8g5rh27DxMaQLy8u+cdCsAOL\njvLDmlNsvrFSWex18bAH60d8zRbPVQTeCWH3rO/YH7AFKxdzvplxgN/3XOSn1G/ZO+cIFw9d40TK\nfiWRbp24hz/2X2G378Z/bDzjcfwW64Ztw6qOBavPLsDA7MWLvJKjU/lhzc9cOHQNhUKg05DWDJz1\nIbbu5UvBrQhkpebgc/UxD6/44+sRQGJkCiBKr7u3EVV1XVs4ip7oe2Z0yWVyUhOySIxJIzEqjYTI\nVJJi0kmMSSMpJl3plT+FpnYNjC31MbHUV0YzjCz0MDTTwdBcF209UZW5KmT0hiGXK0hPyiIpJr2E\nLNJJjs0gMVr8IdMSs0qNr6FZDVNrA0ytDTC3NcTM1hBzOyMs7IzQfk+ktfNznhBwOwS/G0H4eAQQ\n+iAChUKgWg0N6rZxoXEXd5p0q4eVi/lr/76CIHDvDx9+WHOKgNshGFrqM3TRx3Qf2eGF14r8bgSy\nqPdatA1rs/HqMowsDcqMKcgvZJSzmJ20xXMVEomE/Ox8BhiNpv+0Xnz0RW8+tZzA8GUDGbp4AKPd\nZmBoacDaPxYy1Fbsh7Ds1BxA9DjG1fsfvcd3VVY8/x1Pq6brtnFh5a9z/7XD29+RkZTFkZU/8cf+\nK0gkEnqM7sTAWX2eu05RUSgukuLvGcz9i754X/Yn0k8sYNPUqSmq5rarg3sbF+zqWb8XGYQyqZyU\nuAziIlKIj0whITKVhKg0EqJSSYnLLBWJUK+mhomlPiZW+phYiRGIp5O/iZUBWjrlk7WoIoRKhqKC\nYpJi0kmISiUpVnT5EqLECyE5Nr2Ud1FDsxpmNoaYPyUJeyMsHYyxsDemRq03G3qpSORl5YtCd9ce\n433Zn9iSBjGGFvo07upO854NadS57mvNYhIEAe9Lfhxc+iNBd8OwdDFj7LqhtOjd6IVIKeheKPO6\nr0LbsDZfeax4pub+2b2X2Dx+N8tOzaZ1v2YAzOm6gsykLPb6fcX01guRSeWs+m0+A03GMHrtZzTs\n7M6UZvOYuXcCPUeLjXEW912H3/VADoVuf2aY6tqPN1nz6VYadKrLil/mvlB4riCvkOMbf+WnTb8h\nLZbRc3Qnhszv90ySq0gkRaVy94+HeJ3z4dGNIIqeFKGuoYZba2cadnSjQQc3HBvbvbMEIAgCGck5\nxIYnExeWTFx4CvERKcRHppIcl1Fq0q9VuwZmtoZKA9HEUg9TawPMbA3RN9GukBBdFSG8Q5DL5CTH\nZRAfkVpiLYhEER+RQnJseil9c30TbSzsjDC3N8LKwQRLR2OsnUzRM679znkVKTFp3L/wiPuXHvHw\nij9PcgpQr6ZOvXZ1aPFBQ1r2bvxC2jwvAkEQuHnai28XHiU2OIFGnd2ZtGUk1q7l7wMccCeEuV1X\nYGJrxObrK8t0JJPL5Ix1n4mquiq7fTaioqKiTDn9LuxrrvzgycElx+g+siPnD15l842VeJ66y687\nzvFj4l60dDUJ9Y5gUpO5jFw5mM8WflzmGO5f8GVxn7XUaeHEmj8WlpsMBEHgyg+e7J33PekJmbT/\npCWjVg3G3OH1NL1RKBQE3g3jzu/e3D37kOiAOADMHUxo0q0ejbq406C9a6VIaX4RyKRy4iNTiAlJ\nIjYsmdjQZOIikomPTKUgr0g5rkatamIUwNYQUxtDzGwMsLA3wszWUBnWeZ2oIoT3BNJiGQlRqcSG\nJhMbnkx8RCrxESnEhSeTl/2n8J2mdg0s7I2VBGHtZIK1sykGpjrvBFHIpDL8PYO5+8dD7v3hQ1yo\nuEDt1MSO1h82oe1HzV/LZCWTyjiz6yKHl5/gSW4hH8/oxdAlA8rdWN37sh8Le63GrbULa88tLJPa\neenIdb4cvp2Vv86jRe/GJEenMtR2Ep+v/pT6HVyZ3lrMInJt5cyGy0sY7foF1q4WrDozH4DVQzZz\n7+xDfojZWSYMFOYTyRdtF2PmYMJX15aXO0wUHRjH1kn78LseiFMTOyZtHolbK+dyffZFIJPK8PUI\nxPP0Pe787k1GYhaqaqq4t3WhWY8GNO/VEAtH0wrf7+uAtFhGXHgK0cGJxIQmEROSRExYEolRaaW8\neyMLPSzsjTC3LfHsHY2xtDdG3+TtVjZXEcJ7DkEQyEzNJTY0ieiQJKJDEokLSyYmNJmsv1RfamrX\nxMbFFGtnU2ycTbGpY4atixm1alc+mYq/IiY4gZunvbj92wOCvcIBsK9vTduPmtN+QAvM7CtWDycr\nNYf983/g3IGrmNgY8sXucTTqUq9cn3066X8wrmuZ1pYyqYzh9lMwczBh45VlAExtMR9BENh2ew2Z\nydkEe4XRsk8T4kIS+LzODKZ9M5Y+E7oRGxzPaNcvGDj7wzIVyZkp2UxuOhcE2H53bbnaREqLZRxb\n9zM/rPmZGprVGbP2M3qM7lihWUNyuYJHHgF4/HSHm794kZOeR/Va1WjSrR6tP2xKs54NXqm38+uG\nIAikxGcSGRBPZFACMcFJRAUnEhee/KdGmKoKptYGWDkaY+kgGmBWziZY2BtX2lT0KkL4DyMnM5/o\n4ESighKIDEwgOjiR6JAk8v8ipW1irY+9qwW2dcywdTXH3s0cIwu9SulNpMSm43n6HtdP3iXwTigA\ndZo70HFQK9oPaIFOBUok+HoEsGXCHuJCEuk9vivjNgwtl7ewf/73HPvy9DNrBJ4Wq22/swaXZo58\nv+okB5cc40TyvlISF0+VTQ+GbMPcwZRtk/Zy7sBVvo/eWUoGQi6TM7vLckK8wtl8Y2W5ehdE+sWw\nbsTXRPhG03FwayZuHlFh0hKi3lQUl4964nHiDhlJWdTQrE7zng1p/0kLGnetVylrAYqLpEQHJxLx\nOJ7IwAQiA+OJCIgv5XkbW+ph5WiCjYsZtnXMsHE2xdze6J3LbnovCUFL31LoMmgxBrqaGOppoq9b\nC32dWhjoapa8VgtDPU20xJZxb/twKxUEQSAtMYvIwAQiAuIJ948jMjCBhMhUpZCXpnZNHOtZYl/X\nAvu6Fji4W2JmY1CptFxSYtO5dvyWKKLmH4uqmirNezWk67C2NOvRoEJakxYVFHNg8TFObTmLuaMJ\n849Mw6nx8ydduVzOot5r8b0WwNd315bK/3+SW8AQi/G06teUuYemEnAnhOmtFrL4+EzaDWipHLd2\n6FZ8rj7mWNxuCp8UMdhsHK37N2POwSml9nVw8TG+X32SeYen0fmzts89LkEQ+HnbWfbN+4FaOrX4\nYtdYWvVt+hJnpSwyk7O5cuwmF77zIOpxHOoaajTt0YBOg1vRrGfDSkUCRQXFRATEE+YXS7h/HGH+\ncUQFJSCXiYu71WpoYONsip2bOXZu5ti7WWDlZEKtSij4+DJ4LwnB2s5FGDtrC6kZuaRm5JGelU9u\nflGZcRrqahjpa2Kkp4WhvibG+lpKEnn60NOphWolmujeFgoLiokOSiTMP5YwvzjC/GKICvpTQrtW\n7Ro41rPEuaENjvUscapvVWnWJaIex3LxyA0ufX+DrJQcdI216Ta8Pb0+74hJBWjq+F57zJcjRKmJ\n8ZuG8+HEbs/93pkp2UxoMAstPU12eK0rVc28deIeLn7nwY+Je6lWQ4N+OiPoNbYLk7aMAqCooIhB\nZuNo+WET5h6ayvmDV9n4+Tdsuraceu1cSx3T7M7L6TaiA7O+nfTc48/NzGPDqJ3cPnOfFr0bM3Pv\n+Ff2ChQKBQ+vPOaPb69w69cHyGVynJva0214O9oPaFkpxBDlMjlRwYmE+sYQ4htD8MNoooITlZk9\nWjo1cahniUNdSxzcLbB3s8C0khk+FY33khCeFTIqKpaSlplPemY+qZl5pGbkkZaZR3JaLmmZeSSl\n5ZCWmY/8b1XGqioSDPREsjA2qI2JQW2M9LWURGJsoIW2Vo1KMfG9aUiLZcSEJhH2KFa8oXyiiQxM\nUN5Q+sbauDSyoU4TW1wa2eBQ1+KtWoMyqYz7Fx5xdv8VvM75IAjQtEd9+k7qTqPOdV/pRs/JyGP9\niB3cPetNl6Ft+WL3uOfKcty/4Mv8Hqv45H99GLdhuPL1gNvBTG+9SJlOOqfrClHJNGQbKioqSqnr\nLy8splGXekxtMZ/8nAL2P96svAYL8gsZV+9/qKqpstN7/XNDWZF+MSz9aCOpsWmMXT+U/lN7vtK1\nnJeVz4XD1zmz6yIJ4cnU1tek67B29BjZASuXipPRfhlkJGcT9DCaIO8oAh9EEuobo9Qvq1W7Bk4N\nrHBpaIODu0gAhma6/7n7+j9DCOWBQiGQlfOE1Iw8UjPzSEnPJSUjj5S0XFLSc0lKzyElLRfZ30ij\nmoYaxgZamBjUxsSwNqaG2pgalpCHgeh1qL2jedIviuJCKREB8QT7RBP8MJrAB5EkxYiqqKpqKji4\nW+LWzB63pna4NrFFx6Diu5uVBymx6fzx7VX++PYKmcnZWDia8tG0nnQZ2valSUuhUPD96lN8t+wE\ndVo4svzn2c+1tLeM380f+y/z9b11yvi+IAiMdZ9JDa0abL+9his/3GDt0G2sv7SEhp3cWfPZFrwv\nPuLHhL3EBicw1n0mE78ayUczPlBud9fMg5zc8nsZr+HvuHv2IauHbKGGVg2WnpiJa0unl/reAEmR\nKfz89TnOHbxGYX4Rri0c6TOhK236NX0relUKhYLY0GQee0Xw+F44j70iSI7NAEBNXRV7NwvqNLHF\nuaE1TvWtMLU2+M9M/gWFUpLTckhKyyU5PYfE1BySUrIxMtBi8mftqwjhRaBQCGRk54tkkZ5Hcnou\nSWkiUSSl5ZCYmk3WXxZlQfQyjPS1RKIwqo2ZkQ7mxtqYGonEoa/z/slT/BWZqTkE+0QTeD+SgPuR\nBPtEIy2SAWBhb4R7CwfqtXLEvbkD+iZvVmOmuEjKjZN3+fnrc4R6R6JjVJv+U3rQZ3zXl25afuPk\nXb4c8TX6ZrqsObvgH9Ng87LyGe06AwMLfbbdXq3sZfB0cfnbwC0YWRkw0GQs7T5pyYzd4/jEeAwt\nejdmzsEpHFh0lGPrfuZYwl4l8YQ9jGRSk7n0Ht+Vad+M/cdjPLvvMlsn7sW+oS0rTs9+KfkKgPBH\n0RzfcIbrJ+8gUVGh46BW9JvSHceGti+1vZeFXK4gMjAev9thPLodiv/dCPKynwCga6iFa4kBUqex\nLfZuFmhUf7cWe18ExVIZyWm5JKZmk5CSQ3xyFokp2SSkZJOUmkNW7rPnpybu1iyY0L3yE4JEIvkf\nsBEwFAQh7d/Gv+0so4JCKUlpOSSXkERSqvhDJJT8TSvRW38KDXU1TAy1MDfWwdxIG3NjHSxMdLAw\n1cXEoDbVXkJkrTKjuFBKyKMYArwieHwvAv974UrtFXNbQ+q3dqJBGycatHZ6Y7FmQRB4dD2Q45vO\ncP/CI2pp16TvpO58NK3nSx1DwJ0QFn+4HhVVFb48v/AfxeOuHPVk7WdbS1UcpyVkMMRivLLHwdqh\nW7l/3peVv85leutFykXise4zRVmMkjRVQRCY1WkZMQFxHAje9o9pmz9u+IV9836gafcGLD7+xUvp\n+4c+jOTIqlPc+d2bmlrV+WBsZ/pO6v7aCgT/DkEQiAtPwft6EA9vBON/N1yZHWdmY0jd5vbUbW5P\nnSa2mNsavlcGlyAI5OYXEpeUTXxyFnFJWcQni4+ElGzSMvP463StpqqiND7NjLSVoW9jAzEMbqj3\nZwSj0oeMJBKJJbAPcAEavwuE8G8oKpaSkCJ6E4kp2SSm5pCQnE18Shbxydk8+YsSoUQChnqamBnp\nYFlCEpYmuliZ6WJurPNekIVcJifMPw7/u+E8uh2K350wCvKKkEgk2Nc1p2FbF5p0rINrEzvUo+q6\nagAAIABJREFU1F9/74nQh5EcW/8Lnj97UUu7Jh9P78VH03q+8MQZExTPvO6rKcwvZP3FxTg8w2oW\nBIFprRaSFpfOgeBtygriqS0XgCCw/c5arh67yZpPtwBi05YjkTsozC9ilMt0xm8czoCZfQC4efoe\nyz7awNSvx/DhpO7PPKYjq05yaOlxOgxsyZxDU15Y0TUmKJ6DS49z85f7aOrW4qOpPflwYrc3QtzZ\nGXl4ewTx4FogPp4hpCdnA2JqdINWTri3dMC9hQOGZv9ea1HZIQgCOXmFxCRkEJOYSWxSFvFJmSWT\nfzZ5T0onyYhzhGhMmhrWVhKAqZE2hnqa5U6MeRcI4SdgJfAL0OR9IITnQRAEMnMKlIyfmJJNfHI2\ncSUXQ0aJGwwiWRjpaWFhqouVqS6WprpYm+lhY66HsUFtVFTeTatIJpUT7BONj2cwPp4hBD6IRC5T\nUEOzGvVbOdKsc12adXZ77eGlCL8YvlvxE7fPPEDXWJvhSwaIIncvsB6UGJnCrE7LKcwv4qtry54p\neeF3I5CZ7ZcwatUQPl3wEQCHl5/g8IoTHI3bjUZ1dSY2moOVqwWD5vSlfns3Di45xtE1p/g+ZhcG\nZnrI5XLGuv8PgL2PNj1TiO+pZ9B1eHv+t2/CC32PzORsvlvxE+cOXKV6rWp8PL0X/af2fOmwWnmg\nUCgI9Y3l3uXHeF0NIOxRLIIgUFuvFg3aONOgtRMN2zpjYvVmvJLXgaJiKdEJmUTHZxCTkEFsYiYx\niZnEJ2eVyoxUVZFgaqSNhYmOGEkw1sHUqDaWJrqYG2tT7RWaGv0VlZoQJBJJX6CTIAjTJRJJFP8B\nQvg35D8pIjYpS3nxxCVnEZeYRUxiJrn5f0reaqirYWmqg5WpHtbmethY6GFrro+Vmd4751Xk5xbg\n4xmCt0cQ968FkhInLg46uFvQrHNdWvZwx97N4rWFBQLuhLJvwVEe3wrG1t2KyZtH4N7GpdyfTwhP\n4ot2S5GoSNjqufKZfZcX9VlLwK1gjkTtpKZWDWKC4hntOoMJm0bw8Re9y4z/3HUG+qY6bLi8DBCF\n61YP2VKmZuEpzn17lU1jd9FhUCvmHZ5abjKQFss4veM8P6w5RVGBlD4TujJkbl90DJ/d4+FVUVRQ\njPf1IO5c8MfrymMyU3NRUZHg0siGRu1daNLRFcd6lu9c6mdmzhOi4tKJjEsnKj6D6JL7NzktRxne\nkUjAxKB2SRRAnPStzPSwMtXF1LA2am+gM+NbJwSJRHIJeNaq20JgAdBNEITsfyMEiUQyDhgHYGVl\n1Tg6Ovq1HG9lRmbOE6JLLrboePGCi07IICE5G0XJ76cikWBuoiOShLkethYG2FnqY2Ou/04QhSAI\nRAcncveSP/cuBxB4PxJBEDC21KNl93q0+aABdRrbVPiEIQgCN07dY++870mJTafLZ20Zu+7Tck+M\nkX4xfNF+Kfpmumy7uaqMZR14N5RpLReUyhia0Gg21WposPXm6lJjEyOSGe4whUlbRtF/Wi8EQWBC\no9lIC6Xse7y5zHf3OufDog+/pGGnuqz8dW65w0R+nkFsm7KfmKAEmvVowPgNQ1+LplB+bgF3L/pz\n649HPPAIpPBJMbVq16Bxhzo07+xGk06u1K4EdQvlQWbOE8Jj0oiMTSMqPoPIuHSiEzLI/ItnX7O6\nunKitzTVxcZCH2szPSxNdSrM0n9ZvHVC+McdSiTuwGXg6Zm0ABKAZoIgJD3vs++zh/AyKJbKiE3M\nIjIuTbRQ4jKIik8nNjFTmUKrqiLB0lQXO0sD7CwNsLcywN7KEDMj7UodespKz+XuBX9u/uHLQ89g\nZMVy9E20afNBA9p/2AiXRjYV6jkUPini6LpfOPHVb9TSrsHEjcPpOLhVufbhe+0xc7uvpkm3+iw/\nPbuMlT6z/RKSIlM4FLYddQ11vlt2nCMrf+JE8r5Scta/7b7I1ol7+DZwC5bO5tz9/QGL+qxj9oHJ\ndBvRodQ2Y4MTmNJiASa2Rmy5vqJc6yD5OU/YN/8oZ/dfwdjKgElbRtCiV6PynaByoiC/iLsX/bl+\n5iH3rwUgLZKhZ1ybFt3cadOrAe4tHN7IetHLoqhYSkRsOuExqYTHpBERl05ETBrpWX8mjGjVqoaN\nuT7W5nrYWRpga6GPjbkeRvpalXaRu9ISQpkDeKGQUUPBy8u70p70ygKZTE5cUhbhsWmERacSHptG\nZGw6CSlZSje2Zg0NHK0NcbQ2xN7aEEdrI+ytDCqlN/HU0rzx20MeeAQhLZJhYq1Px35N6PRxUyzs\nKq6JS9TjWLZM2kfg3TBafdiE6TtGl8tb+HXnebZP+ZbPFn7EyBWDSr1396w3i3qvZe53U+kytJ1S\numLRjzNp/8nfpCuu+HMsfg8SiYS53VcSGxjPd+Ffl5LkKMgrZHLz+eSm57Hj3lqMrP69d4HPtcds\nHLOb9IQMPprei2GLPqowqWm5TI739WCu/nyfW+ceUVRQjL6xSN7tPmyIS6OK9+wqAhnZTwiJTCEs\nOoWw6FRCo1OJSchAXiI3X01DDVsLfWwt9HGwNsTByhBbS/13Mp38/SSE+tWFe+cdQNUIVIxB1QRU\nDJGoGoFKyUPVGFSMkai8vkWxdxUFhVIi49IJi04hJEp8RMSk8aSkqlNVRYKthQEu9sY42RjhbGuE\no40R1SuRkFd+TgG3zj3iyikvHt0KRaEQcG1iS7dBLWjTu0GFaM/I5QpObT3LoWUn0NLTZNbe8TTu\n+nzlU0EQ2DRmFxcOebDu/EIadXZXvqdQKBjj9gVaeppsvbkamVRGf92R9Pi8E5O3fQ6IVciDzcbR\n+qNmzDkwhaSoFIbZTWb4soEMW/JJqX2tH7mDy9/f4MsLi2jQse5zj0smlXFo+U+c2PQbZvbGzN4/\ngTrNHV/yzJRGbFgyl07c5dJP98hIzkFTuyZtPmhAp4+a4NbMrlKRQGpGHsGRyYREphAcmUxQRDKp\nGXnK9431tbC3NsTJxghHG3HyNzPWfm/kbd4ZQngRNGlkI9y7NhEUKSBPAkUyKNJAeFJ2sESrhDBM\nQNUEiapJKcJA1RQkb1ejvDJAoRBISMkmNDqF4MgUQiKTCQpPVha5qEgk2Frq4+ZoSh17E1zsjLG3\nNHgjC2H/hvSkbK6c8uLi8bvEhiVTrYYGHfs1ptew1jjWe/UewBF+MawbsYPogDiGzO3LsCUDnrto\nW5BfyORm88nPLmCPz/pS4aDjG35h79wjHAjehoWjKfN7riI6II7D4TtQVVNV1i1svLqM+u3d+Hbh\nD/z45WkOR+zAyOrPxeorR2+ydug2hi7+mBHLBj73+FNi01kzbDuBd0Lp+XlHJmwY+speQXGRlJtn\nfTl75Cb+d8NRUVWhaSdXun7SnKadXSuFCmhufiGB4UkERSQTEJZEQFiiskZIIgFLU11c7ExwtjVS\nEkBtzfdDxO6f8H4Swj+sIQiKvBKSSBZJQp6CoEgWSUOeCIokUKQDf/uukholhGEKqmZIVM1AxVQk\nElUTUDH9T3oagiCQlplHUIRoST0OTSQwPEmZLldNQw0XO2Pcnc2o62iGm6Mp+m9R414QBIK8ozh/\n9DbXTj+gqFCKU30rPhzVjrZ9Gr7SJFVUUMyOGQc5f8iDRp3rsuDItOfm5of5RDG1xQLaDWjB/CPT\nlK+nxafzmfVEBs7uy+i1n3Hj1F1WDNjIqjPzaP5BY1Z8spGA2yH8ELMLuUzOp5YTqNPSiRWn5yq3\nkZmSzWi3mVg6m/HVtWXP7QXtdyOQlZ9uo7igmBk7x9Dhk7IZSi+C1IRMfv/Okz9+uEVORj4m1vr0\n/LQVXT5pjp7R68lMKg/kCgVRcek8Dk3EPzQRv+AEohMylO9bmOjg6vDUmBE93ppvQXLjbeM/RQjl\ngSBIQZFaQhpJIE9GeEoW8gTxoUgt+0GJDqialTwskKiag6r5n6/9R7wMQRCIT84mMFy0uPxCEgiJ\nTFEuXpsZaVPP2ZwGdcyp52KOtdnb6a2Qn1PA5ZNe/HboBrFhyegYaPHhqHZ8MLzNK2W0/PHtVb6e\nfgATGyNWnJ6Fuf0/d287vOIE3y3/idW/zaNZz4bK15f2X0/A7RCOxu5CEAQGm4+nUdd6zD00hY/0\nR9Hp07bM2DWOW796sbTfeiVZPMXqIVu4edqLnd5fYl3nn1t9nj/kwdbJ+zG1M2LpiZlYOZu99PcO\n84vl5K4rXP/tIYJCoEU3dz4Y3pqGbZ3fSkiosEhKYHgSvkHx+AbF4x+SQH5JwWdtzerUdTKjrqMp\nbg6mONsZU/slqrXfRQiCrMQoLpnL5PEI8niQx4OqJao6K6sI4UUhCMUloaikEu8iAUGeBIqSEyuP\nB6G0XgiSWiUEYQ6qlkhULUHVsuS5BRKVdyOt7mVQVCwlJDIFv5BE/EMS8AmKU+o9aWtVp4GLBQ3d\nLGnsZomthcEbzWpSKBT4eIbw895r3L8aQLUaGvT8rBUfjev40hWvfp5BrBi0GYmKCqt/mYNjo2fr\n+hQXSZnYeC7FBcXs8/9KKap36xcvlvZfz+rfF9CsZ0M2j9vF1WM3+WLPBNZ8uoWlJ2fRpn9z1g3f\nxr2zDzmeuFe5mOx13ocFvdYycsXAZ/ZWBpG0v1/zM4dXnqRxF3cWfj/tpQrMBEHAxzOEH7++iO/N\nEGpoVqPnZ635cGRbjC3fbLFYQaEUv5B4HvjH8jAwlqDwZKURYmdpQH0Xc+o6meHmYIKl6furYioI\nghgel8eDPBbksQjy2JLncWIkBHnpD6noi0arejNUtedVEUJFQxAEEDJLfoSnLJzwlx8lDoTSekZI\ndEDtKUlYIVG1BjUrULUWF8TfowtYEARiEjPxC47HJzAen8A4ElJEGQJtreo0rGNJE3crmtWzxtz4\nzfVUiApK4OTuK1z9+T4SiYSuA5szZHr3lyKG2JAEFnywjrysfJafnEW9dnWeOc732mNmdV7BqFWD\n+XR+f0Akik+MR9P+k1bM3DtBmVYKoKlTi0Nh26mpVYOBJmNo8WET5hwQG+PIZXImNJpDcaGUvX6b\nnhkCEwSB3XOO8PP2c3Qd2pYZO8e8cLMgQRDw9gji8KazBD+MRt9Ym35jOtDzs1ZvrOWqVCbHPyQR\nL79oHvjHEBCehFyuQFVVhTr2xjSoY0F9Z5EEtN+T5jVPIRqk8SCPBlkMgjxanPxlseLcwt96v6gY\ngaqF0iCVqJqV/G8qPpf8eX6qQkZvAUrCePoDyuNLWPzpI4HSLF4d1CxEclC1RqJmA6q2oGYDKkbv\nBVkkpmTzMDCOhwGxPHgcS1JqDgDGBlo0c7emeQNbmrpboVVBKZDPQ3JsOid2Xub8sdsA9PqsNUOm\nd39hqe60+Azmf7CWpKhUVpyaRcNOz870WdJvA74ej/kudJtygXnloK/w9wziWNxupEVS1ny2Fes6\nFvSe0A1DC33u/PaAxR+uY/npObT6UOxsdmbXRbZN3seSEzNp+1HzMvtRKBTsmHGI3/Zcot/k7ozf\nMPSFwzmPvSI4sPZXHt+LwMhcl0FTu9FlQLPXrh761Ii48zCSu4+i8AmMo7BIhopEQh17Exq5WdLQ\n1YJ6LubvRexfnPRjQRYJ8igEWRTIY0AWLUYm/rrOKakFqlYlxqQFkqeTv1rJc0n575kqQqiEEASp\n6NrJo0osgFjxYpDHihfEXy0ASY2Si0EkCImaLajagZo9EhXNt/UVXgmCIBCXlMW9R6L1d98/hrwn\nRaiqSHB1MKVlQ1taN7LDwfr1ek4p8Rkc3XqBCz/eoVp1dQZO6Ur/MR1eqF9CVmoO83quISE8mbW/\nz8OtlXOZMdEBcYxrMJu+k7szafNIAC4duc6Xw7fzlccK3NuW9S5Wf/q0L8Ie1NTVKCooZpj9FCyc\nTNl0dVmZ8yIIArtmH+H01+cYOKsPn68c9ELnLj4ihW/X/Mqtc4/QNarNp9O7021wi9eaLVRULOW+\nXwy3HkZyxyeSxBIjwcpUl6b1rGlS14pGbpZvxEh4HRDDO8kgCwdZOII8EmRRouUvTwD+0ndFoisa\ngCWhZomaZYmBaAMqFbcOV0UI7xgEQVFyEUWALBJBHlNCHNEiafzVs1AxghKCkKjZg5o9qDm8c16F\nTK7gcWgCd3yiuOsbRVBEMiB6D60b2dG2iQON3SxfW4prXHgyB9ae4da5RxhZ6DFuaX9a9ahX7nOY\nlZLNzE4ryE7LYdPlJdi4WZYZs2nMLi7/4MmRiK/RM9GhIK+AgSZj6Tq8fZm+BtJiKQMMR9N+oBhS\nAji94xw7ph1g45Wl1G9ftinO0S9/4eDS4/Sf2oPx64eW+9jzcws4tvUCp/dfQ01dlYGTu9J/bAel\nKmtFIzPnCTe8wvD0juC+XzSFRTJqVFOnsbsVLerb0KKBLWav2N7zTUM08KJBFgayMISSexd5VOnQ\nsaTWn56/qjUSNeuS57ZIVN5MhlYVIbxHEC+8mBKyCCtxMyPF50LOnwMl2iXkYIdEzQHUnMTHO7JW\nkZaZxy3vCG56R+BVMmlo1apO60Z2tG/uQIv6Nq9FE8b3Zgi7lp4iKiiBJh1dmbLmk3IvniZFpfJF\nx2WoqKiw/eZK9Ex0Sr0fH5bEKJcZDJnfj1ErBwOwYuAmHt8M5mjsrlKhHZ+r/szuvFwZLpIWyxjp\nPB0DCz22XF9R5je8/IMn6z/fSafBrZn97YRyhYkEQcDzdx92Lz1FenI2XQc1Z+TcPq8ldTQ5LYdr\nd0O5fj8M38B4FIKAiWFtWjeyo01jexq6WqDxguscbwOCIBMneWkIgixUtPzl4aLVj7RklKQkfv/U\no7cDVfFerAz3XxUh/AcguqbpJRZKaOmLVfFnLjYSXVB3BjVHJGpOoOYMak6VusaiqFjKvUfReNwL\nw/NBODl5hdSsoUGbxvZ0aeVM8/o2qFeg5yCXyfn14HW+W/87ggAj5n5A38/bl2uSDfeN4ouOK7Cv\nZ8WX5xeWCbcsH7CJh1f8+T5qB7Vq1+TCoWtsGLWDnd7rcWjwZ6bSwSXHOLr2Z06lH6BW7ZqcP3iN\njaN3lklfBQjyCmdWl5XUaebAmt/nlUvYLiM5m+3zf+TOBX/s61owZc1AXBrZlO8ElRPpWflcuR3M\nlTsh+AbFA2I2UPtmDnRo5vjaw4GvAvF+SgFZMEiDEWQhIAsV7y+e9jJREcM7JZ65RM0R1BxFI0xS\neRe5qwjhPw5BkQHSUJAFI8iCSi7s0L9UdUvEOKW6KxI1Z1CvA2quSFTLSji/bchkcrwDYrl8KxgP\nrzBy8gqprVmdzi2d6dG2DnWdzCpskkmJz2DHghPcu/yYus3tmbVlaLm8hesn77L6s230GtOJ6V+P\nLvVe8P1wpjRfwMSvhvPR9A9Ii09niOWEMhLYU1vMR6EQ2HFPzDya1HQe0mIZe3w2lPp+Wak5TG6x\nEFU1VbbfXIl2ORbFr5/xZvu84xQXShk2uxf9x3R4bmHbi6CgUMq1e6GcvxHAfb8YFIKAnaUBXVo5\n07mlM5amla+xjSDIxPCOLFC8P6RBIAsobUipGJdM9s5I1J1LPG57JJLXE1Z7nagihCqUgSAoxOwn\nWTCCNBBkgeKNoIj/c5CKEajXRaLuBmquoO4makNVEqtOKpNz71E0528EcON+OEXFMixNdfmggxs9\n27liqPdiGUPPgiAIXPrpHruWnARgypqBdOz/r/cS+xcd4/jGMyz6YVqZbKDpbRaTm5nHfv+vkEgk\nDHeYgrWbBSt/mQeg7JMwbsNwPvlfH8J8opjYeC6Tt42i3+QepY5tSf+NPLziz5bry3FoYPPcYyp8\nUsQ3i37i4vG7ODe0ZtbWYRUiBigIAo+C4/n92mOu3A7mSaEUE8PadG9Th25t6mD7hlpulgfi5B8G\n0scIsgCQPgZpAPC0z4i6uAan7opErU6JceSEROXdWtN4HspLCJU/gFeFCoNEoiLWQKhZIaneVfm6\noMgpcZMfI0gfg9QPoegqyhQ4FSMEdXck6vVB3R3U3d/YYtjfoa6mSutGdrRuZEd+QTHX7obw21V/\ndh31ZM+xm7RubEf/rvVpVs/mpQvhJBIJXT9pTr0WDqyfdpj1U7/D704YE5Z//Nw0zBFLB+DrEcCW\nSftwbmJfSoW0+8gObB6/h2CvcFyaOdCmfzNObvmdtIQMDMz0uHrUExUVCZ0/awPAb7suoFFdnU6D\nW5fax6+7LnLvnA+TNo/4VzKICU1i9fhviQ1NZsj07nw6o8crS0/n5BVy7kYApy/6EhWfQY1q6nRu\n5Uyv9m7UczZ/65LqgiCIWXvSRwhSP5D6lp78JTVBzQVqDkai7ioaPWq2SCRvX4OpMqDKQ6jCMyEo\n8kEWVEISj0D6SFxYewpVO9BohES9IajXBzUHkXDeEuKSMjlzxZ8zV/3IyinAzFibj7s1oHfHuq+U\nviiXyfluw+8c33EJp/pWLN43BgNTnX8cnxCezMRm86nb2plVv8xRelZ5WfkMsZxIxyGtmblnPPFh\niYx0msboNZ8yeF5/xjeYhaZuLTZdXc6T3AIGmY+nw8BW/G/fBOW2kyJTGNd4HvXaurDy9Oznem23\nzj1i4/TDaFRXZ+6OETRsUzYt9kUQHpPK8T8ecv5GIMVSGa4OJvTrUp/OLZ2p8ZprFZ4HQZEPUj+Q\n+iBIH0Kxj1gLBICG6OGq10Oi7i7+r2qDRPL2hRnfNKpCRlWocAiKbJD6l1hfT2++LPFNiRaoN0Ci\n0RQ0mohexFuItRZLZXjcC+PUBR98g+KpUU2d3p3qMrhXY0xfIa3x6QRbQ7Mayw+Ox8G9bIrpU5ze\ncY6d/zvM3AOT6DTkTwt/09hdXDt2i+OJe6ihWZ3prRdSmF/E6rMLGGIxnrFfDmXg7L5cOOTBhs+/\nYavnSlxbOgGi5Tv/g3UEe4Wx23s9Rv+wriEIAie+ucSBtWdwqm/For2jX1qqQxAE7vpGc/Q3L7z8\nYtBQV6NHuzr071ofZ1vjl9rmq0KQp4H0AULxfSi+LxotT1OyVe1Ao2GJJ1tPTKKosvyBKkKowhuA\nuCYRJVpnxT4gvV+SkQGgLoaXNJoj0Wgh3qgvUFlZEQiOTOb4WW8u3AwCQaBzS2eG9WuOfTkayjwL\nkYEJLBu5m9zsJyzZP5YGrZ2eOU4uVzCz4zISI1P51m8jmiVKsH43ApnZYRnzD0+l06dt+OmrM+ye\n9R1m9sYkhCfzzf0vcWxkx+IPvyTSP5bD4duVXsC1E7dZO+xrpmwdSZ/xXf9xv7uW/MRvhzxp37cR\nMzd99lKVxnKFgsu3gzl8+h7hMWkY6GrySc+G9O3s/sZlogV5MhTfQyi+LRKA0kutDhoNQL0xEo0G\nohegUvkWrysLqgihCm8FgiIDir0Rih+A1Ev0KFAgEkR9JNVagkabEg/izSxhpaTn8uPZB/xy6RFP\nCqW0b+rAmIGtsLd68YyqtMQsFg/dSVxkCgt2jqJl92c3zgl9GMnUVosZ8EUvxqz5FBAlJoZYTcKt\nlRNLjs8kLjSRUc6iRPbA2X0Zs+4zCvOL+MRkLD1Hd2Ly1lGAKME9tv5sNHVrsf3Wqmf2ZJDL5Gyc\ncYRrpx8wYEJnRi3o88LyFXKFgks3g/n25G1iEzOxtdDn0z5N6NamToWm+D4PgiIbiu8gFN2C4jti\nvQ2IHqhGUyQaTUC9Mai7IZG8+1IWbwpVhFCFSgFBkQvF9xGkXlB0B2SPAUGs3tRojqRaW9BoJ5bs\nv2Zk5xZw4g9vfjzrzZPCYjq3dGbcoDZYmPzzmsCzkJv1hMXDdhL6KJZ5O0bQtnfDZ45bP+obbvx8\nj/1+m5Qhnk1jd3Hj5F1OJO1FXUONUO8ITGyN0NIV5Uiehos2eyynbhsXAH7c8CvfLv6RL/9YQIOO\nbmX2I5fJWT/1O66fecjIeb0ZNKXbC30fQRDwfBDOrqOeRMal42htyKiPW9KuqcNrXyQWBJnoYRZd\nhyLPv10fTZFoNAeNZmJK9H8w9l9RqCKEKlRKCIpMKLpdEgK4WaLiiFjhWa09kmrtQaPZa4395uQV\n8MOZ+/x41hu5XMHHPRoy6qMWL6Sd/ySvkMXDdhH8MIol+8fSrHPZiTo5OpXR9WbTYWBLZu0dD8Dd\nsw9Z1Gcdy07OonW/pmU+s6DXWmJDEvgudBsSiYT87CcMc5pO3dbOrDg1q8x4hULBxulHuPrzfcYs\n7sfH4zu9wJmAgLBEth/2wDcoHitTXcYOak3H5k6vlQgERQYUXkUo8oDiWyXV9qqg3gA0WiKp1kr0\nJqvi/xWGKkKoQqWHmCIYBUUeCEU3oPguUCyGB6q1QVKtM1TriETl1WsLnoXUjDz2nbjFb1f9qK1Z\nnfGD29KnU91y99HNzy1g3sDtxIYms/bHKdRpXLY/wu45Rzi94zwH/DdhYmuEXCZnkPl4Gnaqy8Kj\nM0pvL+cJA4zG0H9aL8atHwr86R18fXsVjg3Lbn/P8lP8vPcaI+b2ZvDU8nsG6Vn57PzhBmc9HqOr\nXZOxn7Sidyd31J7TIvRVIMjCofAiQtE1kPoACrHmpVq7Ei+xzWv7natQRQhVeAchKJ5A8S2EoitQ\ndE1sCII6aLRAUr0bVO+KREWvwvcbEpXC5gNX8A2Kp469CXPHdcXJpnzFW1lpuczsu5n8nAI2n5mJ\nmU3pdYn0hEyGOU2nz4SuTNw4DICvxu3G4/htfkrZV0py4tYvXiz9aCMbLy+hfgc3CvMLGe48A8dG\ntqz+dS5/xy/7Pdi19CR9P2/P+OUflat4UKEQOH3Jl11HPSkskjK4d2NG9G9BrRdQei0PBEEQq4AL\nL0DRRbFKHkCtrugJVu9SEgaqHAWP7zvKSwhvL3G8ClX4GyQqNZFU74KK9hokhp5I9H6EmsNE3fic\nxQgprVFkjEZ4clIspqsgONkY8c2yQSyd0ouktBxGzz/CrmOeFEtl//pZHQMtVh2ZiEIhsHL0Pgry\nSzcx0TfTpeOgVvyx/wpZJTLPzXs14kluAYF3QkqN9fUIQKO6OnVKUk3PH/IgOy1X2WA3QFCWAAAM\ngUlEQVTnr/C+HsSe5ado2d2dsUv7l2tijU7IYNKyY2zcfxkXO2OObBzBpE/bVSgZCLIwFLnbENJ6\nIqT3g/xdooyz1iIkhtdRMTiFitZ0JOpuVWRQCVFFCFWolJBIVJBoNESl9jwkBpeQ6J+GWqNBHomQ\nMx8hpRWKzGkIhZdFNdhX3p+E7m3rcPSrkfRo58p3P9/l8/nfExb9jD7bf4OZrSHzd44kJjSJzf/7\nnr973YNm96GooJiz+y4DUL+DaBn7egQoxwiCwJ3fvanb2gWNauoIgsCvOy9Sp7kDbi1Lp7emJmTy\n5eRDWDqaMHvb8GdmHf0VgiDw07mHjJhzmMi4dBZP6sHWRQOwMqsYb0uQpyLkH0SR1h8hrRfk7wBV\nQyS1VyAxuoWK3mEktYYjUf3nPtRVqByoIoQqVHpIJBIk6q6oaM1CYnAZid4JqDkIpPcQsiYipLZF\nkbMWQRry7xv7F9TWrMHCiT3YMLc/2bkFjFn4PSf+8C4zyf8djdq5MGJOb2785sO5H26Xes/KxZxG\nnevyx7dXUSgUaOrUwraeFffP+yrHPL4ZTEJYEl2GthWf3wohLjSRXqNLLxLLZXK+nHIIabGMRXtH\nU6PW84v/snMLmL3+NF8duEJjN0u+3zSSnu1f3ToXBClC4UUUmRMQUtsh5K4BQKK1EImhp0gCNQe/\nlhBfFV4fqgihCu8UJBIJEo36qNRejMTwBhKd3aDeBJ4cRkjvjSJ9MELBLwhC0b9v7Dlo3ciO7zYM\np6m7NZsPXmXh5jPkPXn+NgdM6kyDNk7sXnaKuPDkUu91G96elNh0HnkEAtBlaFsCbocQ6R8DwNUf\nb1GthgZtSkTxfttziZq1a5QRyTu+4xKP70UwZe3AfxWpCwhLZOTcw3g9imbmqE5snNcfA91X67Yn\nyONR5G5BSO2AkDVZlI2o9TkSg7OoGPyMpNaISqmYW4XyoYoQqvDOQiJRR1K9Iyq6XyMx8kSiNRcU\n6QjZsxFS2qLI3YggT3zp7evWrsn6Of2YMrQ9N7zCGLPwe6ITMv5xvIqKCrO2DEOjmhqbZx1Fofiz\nVWLLPo3R1KnJ2W+vACJBqKmrcuGQB4IgcPvMfRp3rUcNzepkp+Vy49Rdug1vT42/pMJGBSX8v707\nD66qPOM4/v0FgcgS1qDWpASqYlOokAp1QYZNQYuACDOKaOtSLFZHhsWCaLGjuFtRa1UGcUUrVQRB\nK7IIVmSrWkBArINWcHQMAWSThOQ+/eMcY6o3CYGbnNyb5zPDTO7hnHOfd+7c+5z3Ped9Xp6b+jo9\nBubRe8gPH1kta/6b6xk1+QXS0sRjt17M0P5dDrtXYGZY4SpiO6/B8nvDvkeCiWHNH0WZy0hrOj5Y\nkMklPU8ILiUorSVqfCVqvQC1eBIadIV907H83sR2jcUObqz0HHHPKzH8/FN58OZh7N57gJE3Pce7\n4VV9PK2ObcZvJ1/AxjVbeO3Z5aXb0xs1pO8lZ7F8zhp279hLs9YZnNqvM8tmreCzTZ+Tv7WgdBGc\nt2avovhgCedc1qP0+JKSGFPHP0+jJumMuvXCct8/FjMeemYptz/6Bp1zs5hxxwhObn94dYfMDga9\nrYJB2M5Lg9IRja9GmUtIazENpfeusdnmrmZ4QnApRUpDDc8grcXDqPUiaHQZFC7BCgYT23E5VrT6\nsM7bJTebx6dcQusWTRhzx2yWrNhc7r59h3ajc/eTeOKOeezavue77SPOovhgCcvnrAGg+wXdyN9W\nwFWdxgKQ17cTAG+/vJrsDj+ifacflx678IWVbH7/v1x9yxCat4r/vP7B4hImP/gqz89/l6H9OnPf\nhCE0a1r12kNmB7B9T2P5fbGvxwPFKGMKavMWaU3HoHrHV/mcLjl4QnApS0dlkZYxEWUuQ03GBgsD\n7RhBrGA4Vriqyuc7rk0zHvnTRfz0J8dw8wPzmf/mB/HfV+Ka24ZR+E0Rz9z3Wun2EzrncGxOJu/M\nC+bSdDuvC40yjubEvHb88e9jOK79MezesZf1//yQ0wbklQ7x7N97gKfveZXcU9vRa0j8R8kLi4qZ\ncM9cFq/YzLUjejDmij5VnmRmVojtewrL743tuQ3qHY+aP4ZazUeNhtV4cUJX8yJLCJKuk/ShpA2S\n7o4qDpf6lJaBmgRDHWp6E5R8hu28NOgxVHEoKaNJOlMnDaVrp7bc/ugC5i5eF3e/7BOO4dxLzmDB\n8yvYtuWrIA6Jrv07s3bpRg7sL6RFm2bM3j6Dv665s/Tm8bIXV1JSXELPYaeXnmvWw4vYmb+HkZPj\nTz4rLCpmwr1zWbn2E/4w8myGn1/x/YXvMyvG9s/C8s/G9kwJ1rZoOZO0Vs+h9F6RrnPhalYkn7Sk\nXsAg4BQz+xlwbxRxuLpFSg+eh89chJpOCBb/KRhMbNc4rOTLQz5PesP63H3DYE7v0o67pi3kjbc3\nxd1v+Oj+NGhYnyfvnFe6rceQX1L4TRHvvBL0Er4/h2DZrBW0zc0qXQ1tV8Ee5kxfSs9Bv6BDl7Y/\neI/i4hIm3T+P1es+ZeLV/RjUJ3711fJY4VKsYCC2+yaodyxq8RRpLZ8O1rVwdU5UqX8UcKeFzwaa\n2VcRxeHqoCAxXIEyF0PjkXDgdWzPXVU6R4P6R3H7mIHk5WYzd/E6YrEfzlNokZnB4Kt6sv2LXRQd\nCCbPdezegba5WXxd5t7Ct0qKS5BEjwu/e9T0s4++5OjGDbl4dL+4cWzZVsD7G7Yy/sq+DOjVsUpt\nsNgObNdosIOo+UOo5QtBeXJXZ0VSy0jSv4G5QH+CxU7HmdmacvYdCYwMX3YE4g/cpobWwPaog6hG\nqdy+VG4bePuSXQczq7R6YLU9MyZpERBvrvqk8H1bAqcBXYFZktpbnOxkZtOAaeE5/3UoBZqSlbcv\neaVy28Dbl+wkHVJV0GpLCGbWt7z/kzQKmB0mgNWSYgQZuvLCMc4556pFVPcQ5gC9ACSdBDQgtbtr\nzjlX60U1zXAGMEPSB0AR8Ot4w0VxTKvesCLn7Uteqdw28PYlu0NqX1ItkOOcc676+IwT55xzgCcE\n55xzoaRMCHWh7IWksZJMUuuoY0kUSfeEn9s6SS9Lah51TIkgqb+kzZI+ljQh6ngSSVK2pDclbQy/\nb9dHHVOiSaon6X1J86OOJdEkNZf0Yvi92ySpwpmHSZcQ6kLZC0nZwDlA+XWWk9NCoKOZ/Rz4CJgY\ncTxHTFI94GHgXCAXuFhSbrRRJVQxMNbMcgnmDf0+xdoHcD0Qv/5I8nsAeN3MTgZOoZJ2Jl1CoG6U\nvbgfuAFIqTv+ZvaGmX27cv1KICvKeBKkG/CxmW0xsyLgbwQXLCnBzL4ws/fCv/cQ/KCkTP1rSVnA\nr4DpUceSaJKaAT2AxwHMrMjMdlV0TDImhJOAsyStkrRMUkpV4ZI0CPjczNZWunNyuwL4R9RBJMDx\nwNYyr7eRQj+YZUnKAboAVa8dXntNJbj4ilW2YxJqRzDZ94lwSGy6pMYVHVArlztKVNmL2qqS9t1I\nMFyUlCpqm5nNDfeZRDAUMbMmY3OHT1IT4CVgtJntjjqeRJA0APjKzN6V1DPqeKrBUUAecJ2ZrZL0\nADABuLmiA2qdVC97UV77JHUiyOprw7r3WcB7krqZ2aHXZ45QRZ8dgKTfAAOAPsmUxCvwOZBd5nVW\nuC1lSKpPkAxmmtnsqONJoDOBgZLOA9KBDEnPmtmIiONKlG3ANjP7tkf3IkFCKFcyDhmlbNkLM1tv\nZm3MLMfMcgg+0LxkSQaVkdSfoHs+0Mz2Rx1PgqwBTpTUTlID4CLglYhjShgFVyaPA5vM7M9Rx5NI\nZjbRzLLC79pFwJIUSgaEvxtbJXUIN/UBKlwRqlb2ECpxuGUvXPT+AjQEFoY9oJVm9rtoQzoyZlYs\n6VpgAVAPmGFmGyIOK5HOBC4F1odl6wFuNLPXKjjG1R7XATPDi5UtwOUV7eylK5xzzgHJOWTknHOu\nGnhCcM45B3hCcM45F/KE4JxzDvCE4JxzLuQJwTnnHOAJwTnnXMgTgnOHSFJOWFf+SUkfSZopqa+k\n5ZL+I6mbpFskjStzzAdhUTjnaj1PCM5VzQnAfcDJ4b/hQHdgHEFhQueSlicE56rmk7DmVAzYACwO\nS6esB3Iijcy5I+QJwbmqKSzzd6zM6xhBbbBi/v97lV5DcTl3xDwhOJdYnxLUoEdSHkE5c+eSgicE\n5xLrJaClpA3AtQRrRzuXFLzaqXPOOcB7CM4550KeEJxzzgGeEJxzzoU8ITjnnAM8ITjnnAt5QnDO\nOQd4QnDOORf6Hwi5HMYgGYLSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff01c5bb898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mm, ss = np.meshgrid(mu_space, sigma_space)\n",
    "\n",
    "rng = np.random.RandomState()\n",
    "x = rng.randn(32) * sigma + mu\n",
    "nll = neg_log_likelihood(x, mm, ss)\n",
    "# m = plt.pcolormesh(mm, ss, nll)\n",
    "plt.contour(mm, ss, nll, levels=nll_min + np.logspace(-3, 5, 15))\n",
    "plt.xlabel(\"mu\")\n",
    "plt.ylabel(\"log sigma\");\n",
    "# plt.colorbar(m);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
